First Principles Example 2: x³

In mathematical discourse, the concept of "first principles" serves as a foundational approach to understanding complex functions and equations. Exploring this notion through the lens of a specific example, consider the cubic function \( x^3 \). By dissecting this expression down to its fundamental elements, we unveil its inherent properties and behaviors without relying on preconceived notions or external assumptions. Analyzing \( x^3 \) from first principles offers a clear pathway to comprehend its fundamental characteristics, paving the way for deeper insights into its graphical representation, roots, and overall behavior across the real number line.